Algorithm 1 SoTMM method for solving problem (5)

Input:  $\mathbf{s}$, $\mathbf{H}$, ${\sigma }^2$. 1:Initialization: ${\mathbf{x}}^0=\mathbf{0}$; 2:Set: $i=0$, ${ϵ}_O>0$. 3:repeat 4:  Compute the precoding factor $\psi$ by (8); 5:  Let $\tilde{\mathbf{H}}=\sqrt{P_T/N_{\mathrm{TX}}}\psi \mathbf{H}$, and use (25) to calculate the Lipschitz constant; 6:  Set: ${\mathbf{u}}^0={\mathbf{u}}^{-1}=\left(1/\sqrt{P_T/N_{\mathrm{TX}}}\right){\mathbf{x}}^i$, ${\xi }_{-1}=0$, penalty parameter $\rho >L$, step size $\mu =L$, $k=0$, ${ϵ}_I>0$. 7:  Define $\mathbf{S}={\tilde{\mathbf{H}}}^H\tilde{\mathbf{H}}$ and extract the largest eigenvalue ${\lambda }_{\max }$ by eigenvalue decomposition of $\mathbf{S}$; 8:  repeat 9:   Compute ${\alpha }_k$ and ${\xi }_k$ by (24); 10:   Compute the extrapolated point ${\mathbf{z}}^k$ by (23); 11:   Compute the gradient vector $\nabla {\mathcal{G}}_{\rho }\left({\mathbf{z}}^k\left|{\mathbf{u}}^k\right.\right)$ by (22); 12:   Compute the ${\mathbf{z}}^k-{\mu }^{-1}\nabla {\mathcal{G}}_{\rho }\left({\mathbf{z}}^k{\left|\mathbf{u}\right.}^k\right)$ and update ${\mathbf{u}}^{k+1}=e^{j\measuredangle \left({\mathbf{z}}^k-{\mu }^{-1}\nabla {\mathcal{G}}_{\rho }\left({\mathbf{z}}^k\left|{\mathbf{u}}^k\right.\right)\right)}$; 13:   $k\leftarrow k+1$; 14:  until A stopping criterion triggers. 15:  Reconstruction $\mathbf{x}=\sqrt{P_T/N_{\mathrm{TX}}}\mathbf{u}$; 16:  $i\leftarrow i+1$; 17:until A stopping criterion triggers. Output:  $\mathbf{x}$, $\psi$.